Fuzzy H∞ filtering for nonlinear 2D systems in the Roesser model

This study focuses on the H∞ filtering problem for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems in the Roesser model. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H∞ performance of the filtering error system. By using a new structure of the fuzzy Lyapunov function, and some analysis techniques, the stability and a prescribed H∞ performance index are guaranteed for the overall filtering-error system, such that the coupling between the Lyapunov matrix and the system matrices is removed. In addition, sufficient conditions for the existence of such a filter are established in term of linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired filter can be characterised. An illustrative example is presented to demonstrate the effectiveness of the developed results.